The Hormander multiplier theorem, II: The bilinear local case

Abstract

We use wavelets of tensor product type to obtain the boundedness of bilinear multiplier operators on associated with Hormander multipliers on with minimal smoothness. We focus on the local case and we obtain boundedness under the minimal smoothness assumption of n / 2 derivatives.

We also provide counterexamples to obtain necessary conditions for all sets of indices.

Keywords

• Bilinear multipliers
• Hormander multipliers
• Wavelets
• Multilinear operators